There are a few basic properties of numbers, and, no, giving throbbing headaches is NOT one of them. The three basic (and my three favorite) properties of numbers are:
1: The Associative Property
2: The Commutative Property
3: The Distributive Property
If you spend the time to study the basic properties of numbers, you will grasp a deeper understanding of why you are able to manipulate algebraic equations – throw out your algebra book, because you will gain a natural ability to rearrange and simplify equations! (Well – just in case, DON’T throw out your algebra book!)
Here I will discuss the Distributive Property of numbers and why I should be uttering such things on a web site about math tricks!
Let’s start out with a general formula which demonstrates the distributive property of numbers:
a(b + c) = ab + ac
The way to remember this property is to think of the number outside of the parentheses as “distributing itself” among the values being added within the parentheses.
So what does this have to do with math tricks? Fair question – let me give you an example of why understanding this property is useful for performing fast mental multiplication. Let’s say we want to multiply 8 x 1531. Sure, it looks imposing, but remember that we can break down the number 1531 to:
1000 + 500 + 30 + 1
Now we can perform the multiplication in this fashion:
8(1000 + 500 + 30 + 1)
From the distributive property, we know that:
8(1000 + 500 + 30 + 1) = (8 x 1000) + (8 x 500) + (8 x 30) + (8 x 1)
Now the problem is in a form that we can easily solve mentally by first multiplying left to right:
8000 + 4000 + 240 + 8
And then performing the simple addition step to arrive at the answer, 12248!
So there you have it, the secret to how multiplication math magic works – Shhhh . . . . .